PML stability in 3D FDTD simulation of electroacoustic wave propagation in piezoelectric crystals with different symmetry class

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Restrictions of the existing methods for the simulation of SAW RFID tags

Modeling restrictions for each of the discussed methods are presented below.

Restrictions of the FEM/BEM method

Although its expansion to 3D modeling is possible, it is a complex process due to the following aspects:
– To consider the interaction between Rayleigh and SH waves, the frequencies at which this phenomenon takes place must be estimated [11].
– To simplify the involved Green’s functions evaluation, a false periodicity in the transverse direction must be introduced [12].
– Optimal meshing strategies are required, as described in [13], to ensure an appropriate transition between different kinds of mesh used in the transducer: triangular mesh in the buses and vertices and rectangular mesh in the remaining regions.

Restrictions of the COM model

The main simplifying assumptions of this model are the following [5]:
– It is developed under the assumption of infinite grating of the transducer: this is not always the case for the IDT of a SAW RFID tag, in which short transducers can be used.
– The grating must be periodic, which limits the design versatility that a SAW transducer can have.
– Waves must be non-dispersive: Phase velocity must be independent of frequency, which is not always true. Dispersive waves arise in devices conformed by layered substrates [1].
– Narrowband analysis is done in a short range around the operational frequency, f0.

Restrictions of the P–matrix method

The main restrictions of this method are the following [7]:
– P–matrix computation for reflective IDTs is very complex.
– Only one type of acoustic wave can be present, either the Rayleigh wave or the SH wave, but not both simultaneously.
– Wave amplitude is considered to be uniform in the transverse direction: it is not possible to consider transverse variations of the IDT, such as apodization of the electrodes or diffraction at their ends.

Restrictions of the Delta function model

This model can only be applied in very simple cases where the following conditions are met [8-10]:
– The problem is one-dimensional: extension to two-dimensional or threedimensional cases is difficult.
– IDTs are non-reflective.
– IDTs are unidirectional: because wave generation is only considered in one direction.
– Propagation conditions are ideal: there is no propagation loss and no diffraction at the electrode ends.
– Waves are non-dispersive: This is not always the case. As stated before, dispersive waves are excited in layered devices.

FDTD for simulation of SAW devices

To the knowledge of the author, FDTD has not been previously applied for simulation of SAW RFID tags. The only publication in this regard is that of the author, in [14]. On the other hand, FDTD has been widely used for the simulation of SAW devices. These devices are employed in applications different from RFID, such as: filters and resonators, piezoelectric transducers and nondestructive evaluation (NDE). FDTD was first proposed for simulation of SAW devices in [15]. The governing equations used in that work are two Maxwell’s equations, the Maxwell–Faraday law ( 2.32 ) and the Maxwell-Ampère law ( 2.33 ), combined with two piezoelectric governing equations, the strain-displacement relation ( 2.34 ) and the equation of motion ( 2.35 ), as presented below.

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Table of contents :

1. INTRODUCTION
1.1. RFID technology
1.1.1. Active RFID tags
1.1.2. Passive RFID tags
1.2. Problem statement
1.3. State of the art of SAW RFID tags
1.4. Scope of the thesis
1.5. Contributions
1.6. Document organization
1.7. List of publications
1.8. References
2. STATE OF THE ART
2.1. Methods for the simulation of SAW RFID tags
2.1.1. Existing methods for the simulation of SAW RFID tags
2.1.2. Restrictions of the existing methods for the simulation of SAW RFID tags .
2.2. FDTD for simulation of SAW devices
2.3. Stability in FDTD simulation of SAW devices
2.4. PML for simulation of electroacoustic wave propagation
2.5. Challenges in the 3D simulation of SAW RFID tags
2.5.1. SH–SAW simulation
2.5.2. Geometric variations in the transverse direction
2.6. Computational complexity of the problem
2.7. References
3. FDTD SIMULATION OF SAW RFID TAGS IN 2D
3.1. Introduction
3.2. Problem statement in 2D
3.3. FDTD formulation in 2D
3.4. FDTD simulation results
Table of contents
3.5. Influence of the electrode thickness
3.6. Conclusion
3.7. References
4. FDTD FORMULATION IN 3D FOR SIMULATION OF ELECTROACOUSTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA
4.1. Governing equations in 3D
4.2. FDTD update equations in 3D
4.2.1. Discretization grid
4.2.2. PML absorbing boundary condition
4.2.3. Stress-free boundary condition
4.2.4. Quasi-static approximation
4.2.5. Obtained FDTD update equations
4.3. FDTD simulation of SAW IDTs in 3D
4.3.1. Problem statement
4.3.2. Simulation results
4.4. PML stability in 3D FDTD simulation of electroacoustic wave propagation in piezoelectric crystals with different symmetry class
4.4.1. 3D FDTD formulation
4.4.2. PML stability verification
4.5. Computation of the IDT input admittance from FDTD simulations
4.5.1. Numerical procedure
4.5.2. Simulated IDTs
4.5.3. Simulation results
4.5.4. Procedure for impedance coupling
4.6. Conclusion
4.7. References
5. CONCLUSIONS AND FUTURE WORK
5.1. Conclusions
5.2. Future work .

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